Advertisement

The European Physical Journal Special Topics

, Volume 171, Issue 1, pp 245–249 | Cite as

The lattice Boltzmann advection-diffusion model revisited

Article

Abstract

Advection-diffusion processes can be simulated by the Lattice Boltzmann method. Two formulations have been proposed in the literature. We show that they are not fully correct (only first order accurate). A new formulation is proposed, which is shown to produce better results, both from the point of view of the Chapman-Enskog expansion or when comparing simulations with an exact time-dependent solution of the advection-diffusion equation.

Keywords

European Physical Journal Special Topic Lattice Boltzmann Method Lattice Boltzmann Lattice Boltzmann Equation Lattice Boltzmann Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Succi, The Lattice Boltzmann Equation, For Fluid Dynamics and Beyond (Oxford University Press, 2001)Google Scholar
  2. B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, 1998)Google Scholar
  3. E.G. Flekkoy, Phys. Rev. E 47, 4247 (1993)Google Scholar
  4. Z.L Guo, B.C. Shi, N.C. Wang, J. Scient. Comp. 14, 291 (1999)Google Scholar
  5. S. Suga, Int. J. Mod. Phys. C 17, 1563 (2006)Google Scholar
  6. R.G.M. Van der Sman, M.H. Ernst, J. Comp. Phys. 160, 766 (2000)Google Scholar
  7. A. Wagner (private communication)Google Scholar
  8. B. Shi, Lattice Boltzmann simulation of some nonlinear complex equations, Computanional Science ICCS 2007, vol. 4487 of LNCS (Springer Berlin, Heidelberg, 2007), p. 818Google Scholar
  9. J. Lätt, Hydrodynamic Limit of Lattice Boltzmann equations, Ph.D. thesis, University of Geneva, Switzerland, 2007 http://www.unige.ch/cyberdocuments/theses2007/LattJ/meta.html Google Scholar

Copyright information

© EDP Sciences and Springer 2009

Authors and Affiliations

  1. 1.University of GenevaGenevaSwitzerland
  2. 2.Tufts UniversityMedfordUSA

Personalised recommendations